Abstract: We investigate the dynamics of Rydberg electrons excited from the groundstate of ultracold atoms trapped in an optical lattice. We first consider alattice comprising an array of double-well potentials, where each double wellis occupied by two ultracold atoms. We demonstrate the existence of molecularstates with equilibrium distances of the order of experimentally attainableinter-well spacings and binding energies of the order of 10^3 GHz. We alsoconsider the situation whereby ground-state atoms trapped in an optical latticeare collectively excited to Rydberg levels, such that the charge-densitydistributions of neighbouring atoms overlap. We compute the hopping rate andinteraction matrix elements between highly-excited electrons separated bydistances comparable to typical lattice spacings. Such systems have tunableinteraction parameters and a temperature ~10^{-4} times smaller than the Fermitemperature, making them potentially attractive for the study and simulation ofstrongly correlated electronic systems.